A constrained model for MEMS with varying dielectric properties

TL;DR

This paper introduces a new constrained mathematical model for MEMS devices with variable dielectric properties, capturing the pull-in phenomenon without model breakdown and analyzing solution behavior over time.

Contribution

It presents a novel semilinear parabolic equation with constraints for MEMS, demonstrating the existence of maximal stationary solutions and the dynamics of solutions over time.

Findings

Pull-in phenomenon occurs without model breakdown due to saturation of the constraint.

A maximal stationary solution exists for large potentials.

Solutions exhibit specific large time behavior, including existence and uniqueness.

Abstract

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a breakdown of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.